May 25 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C5 can only be <6>
R5C2 can only be <6>
R6C7 can only be <6>
R4C3 can only be <9>
R4C7 can only be <8>
R5C5 can only be <5>
R6C5 can only be <1>
R5C8 can only be <7>
R6C3 can only be <4>
R3C8 is the only square in row 3 that can be <6>
R7C3 is the only square in row 7 that can be <6>
R7C7 is the only square in row 7 that can be <2>
R7C8 is the only square in row 7 that can be <1>
R8C3 is the only square in row 8 that can be <2>
Squares R1C3 and R1C9 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C1 - removing <5> from <145> leaving <14>
R1C7 - removing <5> from <145> leaving <14>
Intersection of column 3 with block 1. The values <78> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain these values.
R2C2 - removing <8> from <3489> leaving <349>
R3C2 - removing <8> from <489> leaving <49>
Intersection of block 8 with row 7. The value <3> only appears in one or more of squares R7C4, R7C5 and R7C6 of block 8. These squares are the ones that intersect with row 7. Thus, the other (non-intersecting) squares of row 7 cannot contain this value.
R7C2 - removing <3> from <3489> leaving <489>
Squares R1C1 and R1C7 in row 1 and R9C1 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 1 and 7 can be removed.
R2C7 - removing <4> from <47> leaving <7>
R3C1 - removing <4> from <1459> leaving <159>
R3C7 - removing <4> from <1457> leaving <157>
R7C1 - removing <4> from <459> leaving <59>
R8C7 - removing <4> from <34> leaving <3>
R3C3 is the only square in row 3 that can be <7>
R9C3 is the only square in row 9 that can be <3>
R2C3 can only be <8>
R2C5 can only be <4>
R1C3 can only be <5>
R2C8 can only be <9>
R8C5 can only be <8>
R3C6 can only be <2>
R2C2 can only be <3>
R8C8 can only be <4>
R3C4 can only be <8>
R5C6 can only be <3>
R5C4 can only be <2>
R7C6 can only be <4>
R7C4 can only be <3>
R8C2 can only be <9>
R9C7 can only be <5>
R9C1 can only be <4>
R9C9 can only be <7>
R3C7 can only be <1>
R7C9 can only be <9>
R1C9 can only be <8>
R3C9 can only be <5>
R3C1 can only be <9>
R1C7 can only be <4>
R7C1 can only be <5>
R7C2 can only be <8>
R3C2 can only be <4>
R1C1 can only be <1>
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